1. The problem asks: Which best explains what determines whether a number is irrational? 2. An irrational number is a number that cannot be expressed as a simple fraction or ratio of two integers. 3. Important rules: - Rational numbers can be written as decimals that either terminate or repeat. - Irrational numbers have decimal expansions that neither terminate nor repeat. 4. Let's analyze the options: - "a number that can be written as a decimal that neither repeats nor terminates" matches the definition of irrational numbers. - "a number that can be written as a square root that does not result in a whole number" is often irrational but not always (e.g., \(\sqrt{4} = 2\) is rational). - "a number that can be written as a decimal that repeats and does not terminate" describes rational numbers. - "a number that can be written as a decimal that terminates and does not repeat" also describes rational numbers. 5. Therefore, the best explanation is: a number that can be written as a decimal that neither repeats nor terminates. Final answer: **A number that can be written as a decimal that neither repeats nor terminates is irrational.**